Problem: Nadia is 2 times as old as Emily. 21 years ago, Nadia was 9 times as old as Emily. How old is Nadia now?
Explanation: We can use the given information to write down two equations that describe the ages of Nadia and Emily. Let Nadia's current age be $n$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $n = 2e$ 21 years ago, Nadia was $n - 21$ years old, and Emily was $e - 21$ years old. The information in the second sentence can be expressed in the following equation: $n - 21 = 9(e - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = n / 2$ . Substituting this into our second equation, we get: $n - 21 = 9($ $(n / 2)$ $- 21)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 21 = \dfrac{9}{2} n - 189$ Solving for $n$ , we get: $\dfrac{7}{2} n = 168$ $n = \dfrac{2}{7} \cdot 168 = 48$.